How do I add a tab detached from an entity's domain?

To build a custom tab you will need to tap into the AdminBasicEntityController.modifyEntityForm(...) method.

In this method, you can add a new tab and even provide a custom html template which can then hold all the elements needed for your custom logic which can be set in a custom admin controller or in the extended product/customer admin controller. Here's an example of how we do this (from the OMS module):